Pour flour into a shallow bowl. Dredge apple chunks in flour.
Mix cornstarch and 2 teaspoons water thoroughly in a small bowl. Mix in egg.
Heat oil in a large saucepan to 320 degrees F (160 degrees C). Dip apple chunks in the cornstarch mixture; cook in the hot oil until browned, about 3 minutes. Transfer to a plate using a slotted spoon.
Combine sugar, 3 tablespoons vegetable oil, and remaining 1 teaspoon water in a separate saucepan over medium-low heat. Cook until sugar melts, turns light golden, and starts to bubble, 8 to 10 minutes. Mix in fried apple chunks until evenly coated with caramel.
Transfer caramel-coated apple chunks to a large serving dish; lift with chopsticks to separate and create sugar threads. Garnish with sesame seeds.